Equation of a Line in Space - Three Dimensional Geometry, Class 12, Math

# Equation of a Line in Space - Three Dimensional Geometry, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Equation of a Line in Space - Three Dimensional Geometry, Class 12, Math Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is the equation of a line in three-dimensional space?
Ans. The equation of a line in three-dimensional space can be represented in vector form as r = a + tb, where r is the position vector of a point on the line, a is the position vector of a known point on the line, t is a scalar parameter, and b is the direction vector of the line.
 2. How can I find the direction vector of a line in three-dimensional space?
Ans. To find the direction vector of a line in three-dimensional space, you can subtract the position vectors of two known points on the line. For example, if two points A and B are on the line, the direction vector can be found as b = B - A.
 3. What is the significance of the scalar parameter t in the equation of a line in three-dimensional space?
Ans. The scalar parameter t in the equation of a line in three-dimensional space represents the position of a point on the line relative to the known point a. By varying the value of t, you can obtain different points on the line. For example, when t = 0, the point on the line is at a, and when t = 1, the point is at a + b.
 4. Can the equation of a line in three-dimensional space be written in Cartesian form?
Ans. Yes, the equation of a line in three-dimensional space can also be written in Cartesian form as a set of three equations. The x, y, and z coordinates of a point on the line can be expressed in terms of the parameters t and the components of the direction vector. These equations represent the intersection of the line with the three coordinate planes.
 5. How can I determine if two lines in three-dimensional space are parallel or intersecting?
Ans. Two lines in three-dimensional space are parallel if their direction vectors are scalar multiples of each other. If the direction vectors are not scalar multiples, the lines are either intersecting or skew (not lying in the same plane). To determine if they intersect, you can set up the equations of the lines and solve for the parameters. If the parameters have consistent solutions, the lines intersect at a point.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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